Knight's Tour Snakes

The two-headed snake image in the banner above comes from Karl Shuker's blogspot that I downloaded on 4/25/2025 at 5:35 pm.

After making four 16-move identical mini-knight's tour circuits, I converted their overlapping pattern into two 32-move mini-knight's tour circuits that look like snakes with two heads, one on both ends of the snake's body.  By adjusting the patterns of the snakes, I was able to  eventually make a complete 64-move open knight's tour.

Step 1:

I first made one complete circuit consisting of 16 moves then copied the circuit and flipped it horizontally to make the second circuit.

Step 2:

I made the third 16-move circuit by flipping the first mini-knight's tour vertically. I copied the third circuit and flipped it horizontally to make the fourth circuit.

Step 3:

I combined all four mini-knight's tours on one board.

Step 4:

I slightly modified the four mini-knight's tour circuits by combining them into only two mini-knight's tour circuits of 32 moves each.  I made the first 32 move circuit then copied it and flipped it horizontally to make the second circuit.  It can also make the second circuit by flipping the first circuit vertically. They both look like snakes with two heads on each end of their body.

Step 5:

I combined the two tours from Step 4 to make the following image.

Step 6:

After combining both 32-move mini-knight's tours, I wanted to keep most of the original pattern but make a single 64 move knight's tour.  I was able to do this by moving one line (knight move) and deleting one line.  In the following image, I changed the colors of three moves to red, orange, and black.

Step 7:

In this step, I moved the red line over the top of the orange line and deleted the black line then recolored all the lines in the tour back to blue to make a single 64 move open knight's tour.